| Commit | Line | Data |
|---|
| b282a552 |
1 | package Math::BigInt; |
| 2 | |
| 3 | use 5.005; |
| 4 | use strict; |
| 5 | # use warnings; # dont use warnings for older Perls |
| 6 | |
| 7 | use vars qw/$VERSION/; |
| 8 | |
| 3a427a11 |
9 | $VERSION = '0.02'; |
| b282a552 |
10 | |
| 11 | # See SYNOPSIS below. |
| 12 | |
| 13 | my $CALC_EMU; |
| 14 | |
| 15 | BEGIN |
| 16 | { |
| 17 | $CALC_EMU = Math::BigInt->config()->{'lib'}; |
| 18 | } |
| 19 | |
| 20 | sub __emu_blog |
| 21 | { |
| 22 | my ($self,$x,$base,@r) = @_; |
| 23 | |
| 24 | return $x->bnan() if $x->is_zero() || $base->is_zero() || $base->is_one(); |
| 25 | |
| 26 | my $acmp = $x->bacmp($base); |
| 27 | return $x->bone('+',@r) if $acmp == 0; |
| 28 | return $x->bzero(@r) if $acmp < 0 || $x->is_one(); |
| 29 | |
| 30 | # blog($x,$base) ** $base + $y = $x |
| 31 | |
| 32 | # this trial multiplication is very fast, even for large counts (like for |
| 33 | # 2 ** 1024, since this still requires only 1024 very fast steps |
| 34 | # (multiplication of a large number by a very small number is very fast)) |
| 35 | # See Calc for an even faster algorightmn |
| 36 | my $x_org = $x->copy(); # preserve orgx |
| 37 | $x->bzero(); # keep ref to $x |
| 38 | my $trial = $base->copy(); |
| 39 | while ($trial->bacmp($x_org) <= 0) |
| 40 | { |
| 41 | $trial->bmul($base); $x->binc(); |
| 42 | } |
| 43 | $x->round(@r); |
| 44 | } |
| 45 | |
| 46 | sub __emu_bmodinv |
| 47 | { |
| 48 | my ($self,$x,$y,@r) = @_; |
| 49 | |
| 50 | my ($u, $u1) = ($self->bzero(), $self->bone()); |
| 51 | my ($a, $b) = ($y->copy(), $x->copy()); |
| 52 | |
| 53 | # first step need always be done since $num (and thus $b) is never 0 |
| 54 | # Note that the loop is aligned so that the check occurs between #2 and #1 |
| 55 | # thus saving us one step #2 at the loop end. Typical loop count is 1. Even |
| 56 | # a case with 28 loops still gains about 3% with this layout. |
| 57 | my $q; |
| 58 | ($a, $q, $b) = ($b, $a->bdiv($b)); # step #1 |
| 59 | # Euclid's Algorithm (calculate GCD of ($a,$b) in $a and also calculate |
| 60 | # two values in $u and $u1, we use only $u1 afterwards) |
| 61 | my $sign = 1; # flip-flop |
| 62 | while (!$b->is_zero()) # found GCD if $b == 0 |
| 63 | { |
| 64 | # the original algorithm had: |
| 65 | # ($u, $u1) = ($u1, $u->bsub($u1->copy()->bmul($q))); # step #2 |
| 66 | # The following creates exact the same sequence of numbers in $u1, |
| 67 | # except for the sign ($u1 is now always positive). Since formerly |
| 68 | # the sign of $u1 was alternating between '-' and '+', the $sign |
| 69 | # flip-flop will take care of that, so that at the end of the loop |
| 70 | # we have the real sign of $u1. Keeping numbers positive gains us |
| 71 | # speed since badd() is faster than bsub() and makes it possible |
| 72 | # to have the algorithmn in Calc for even more speed. |
| 73 | |
| 74 | ($u, $u1) = ($u1, $u->badd($u1->copy()->bmul($q))); # step #2 |
| 75 | $sign = - $sign; # flip sign |
| 76 | |
| 77 | ($a, $q, $b) = ($b, $a->bdiv($b)); # step #1 again |
| 78 | } |
| 79 | |
| 80 | # If the gcd is not 1, then return NaN! It would be pointless to have |
| 81 | # called bgcd to check this first, because we would then be performing |
| 82 | # the same Euclidean Algorithm *twice* in case the gcd is 1. |
| 83 | return $x->bnan() unless $a->is_one(); |
| 84 | |
| 85 | $u1->bneg() if $sign != 1; # need to flip? |
| 86 | |
| 87 | $u1->bmod($y); # calc result |
| 88 | $x->{value} = $u1->{value}; # and copy over to $x |
| 89 | $x->{sign} = $u1->{sign}; # to modify in place |
| 90 | $x->round(@r); |
| 91 | } |
| 92 | |
| 93 | sub __emu_bmodpow |
| 94 | { |
| 95 | my ($self,$num,$exp,$mod,@r) = @_; |
| 96 | |
| 97 | # in the trivial case, |
| 98 | return $num->bzero(@r) if $mod->is_one(); |
| 99 | return $num->bone('+',@r) if $num->is_zero() or $num->is_one(); |
| 100 | |
| 101 | # $num->bmod($mod); # if $x is large, make it smaller first |
| 102 | my $acc = $num->copy(); # but this is not really faster... |
| 103 | |
| 104 | $num->bone(); # keep ref to $num |
| 105 | |
| 106 | my $expbin = $exp->as_bin(); $expbin =~ s/^[-]?0b//; # ignore sign and prefix |
| 107 | my $len = CORE::length($expbin); |
| 108 | while (--$len >= 0) |
| 109 | { |
| 110 | $num->bmul($acc)->bmod($mod) if substr($expbin,$len,1) eq '1'; |
| 111 | $acc->bmul($acc)->bmod($mod); |
| 112 | } |
| 113 | |
| 114 | $num->round(@r); |
| 115 | } |
| 116 | |
| 117 | sub __emu_bfac |
| 118 | { |
| 119 | my ($self,$x,@r) = @_; |
| 120 | |
| 121 | return $x->bone('+',@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1 |
| 122 | |
| 123 | my $n = $x->copy(); |
| 124 | $x->bone(); |
| 125 | # seems we need not to temp. clear A/P of $x since the result is the same |
| 126 | my $f = $self->new(2); |
| 127 | while ($f->bacmp($n) < 0) |
| 128 | { |
| 129 | $x->bmul($f); $f->binc(); |
| 130 | } |
| 131 | $x->bmul($f,@r); # last step and also round result |
| 132 | } |
| 133 | |
| 134 | sub __emu_bpow |
| 135 | { |
| 136 | my ($self,$x,$y,@r) = @_; |
| 137 | |
| 138 | return $x->bone('+',@r) if $y->is_zero(); |
| 139 | return $x->round(@r) if $x->is_one() || $y->is_one(); |
| 140 | return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0) |
| 141 | |
| 142 | my $pow2 = $self->bone(); |
| 143 | my $y_bin = $y->as_bin(); $y_bin =~ s/^0b//; |
| 144 | my $len = CORE::length($y_bin); |
| 145 | while (--$len > 0) |
| 146 | { |
| 147 | $pow2->bmul($x) if substr($y_bin,$len,1) eq '1'; # is odd? |
| 148 | $x->bmul($x); |
| 149 | } |
| 150 | $x->bmul($pow2); |
| 151 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
| 152 | $x; |
| 153 | } |
| 154 | |
| 155 | sub __emu_band |
| 156 | { |
| 157 | my ($self,$x,$y,$sx,$sy,@r) = @_; |
| 158 | |
| 159 | return $x->bzero(@r) if $y->is_zero() || $x->is_zero(); |
| 160 | |
| 161 | my $sign = 0; # sign of result |
| 162 | $sign = 1 if $sx == -1 && $sy == -1; |
| 163 | |
| 164 | my ($bx,$by); |
| 165 | |
| 166 | if ($sx == -1) # if x is negative |
| 167 | { |
| 168 | # two's complement: inc and flip all "bits" in $bx |
| 169 | $bx = $x->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc |
| 170 | $bx =~ s/-?0x//; |
| 171 | $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 172 | } |
| 173 | else |
| 174 | { |
| 175 | $bx = $x->as_hex(); # get binary representation |
| 176 | $bx =~ s/-?0x//; |
| 177 | $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 178 | } |
| 179 | if ($sy == -1) # if y is negative |
| 180 | { |
| 181 | # two's complement: inc and flip all "bits" in $by |
| 182 | $by = $y->copy()->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc |
| 183 | $by =~ s/-?0x//; |
| 184 | $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 185 | } |
| 186 | else |
| 187 | { |
| 188 | $by = $y->as_hex(); # get binary representation |
| 189 | $by =~ s/-?0x//; |
| 190 | $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 191 | } |
| 192 | # now we have bit-strings from X and Y, reverse them for padding |
| 193 | $bx = reverse $bx; |
| 194 | $by = reverse $by; |
| 195 | |
| 196 | # cut the longer string to the length of the shorter one (the result would |
| 197 | # be 0 due to AND anyway) |
| 198 | my $diff = CORE::length($bx) - CORE::length($by); |
| 199 | if ($diff > 0) |
| 200 | { |
| 201 | $bx = substr($bx,0,CORE::length($by)); |
| 202 | } |
| 203 | elsif ($diff < 0) |
| 204 | { |
| 205 | $by = substr($by,0,CORE::length($bx)); |
| 206 | } |
| 207 | |
| 208 | # and the strings together |
| 209 | my $r = $bx & $by; |
| 210 | |
| 211 | # and reverse the result again |
| 212 | $bx = reverse $r; |
| 213 | |
| 214 | # one of $x or $y was negative, so need to flip bits in the result |
| 215 | # in both cases (one or two of them negative, or both positive) we need |
| 216 | # to get the characters back. |
| 217 | if ($sign == 1) |
| 218 | { |
| 219 | $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/; |
| 220 | } |
| 221 | else |
| 222 | { |
| 223 | $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/; |
| 224 | } |
| 225 | |
| 226 | $bx = '0x' . $bx; |
| 227 | if ($CALC_EMU->can('_from_hex')) |
| 228 | { |
| 229 | $x->{value} = $CALC_EMU->_from_hex( \$bx ); |
| 230 | } |
| 231 | else |
| 232 | { |
| 233 | $r = $self->new($bx); |
| 234 | $x->{value} = $r->{value}; |
| 235 | } |
| 236 | |
| 237 | # calculate sign of result |
| 238 | $x->{sign} = '+'; |
| 239 | #$x->{sign} = '-' if $sx == $sy && $sx == -1 && !$x->is_zero(); |
| 240 | $x->{sign} = '-' if $sign == 1 && !$x->is_zero(); |
| 241 | |
| 242 | $x->bdec() if $sign == 1; |
| 243 | |
| 244 | $x->round(@r); |
| 245 | } |
| 246 | |
| 247 | sub __emu_bior |
| 248 | { |
| 249 | my ($self,$x,$y,$sx,$sy,@r) = @_; |
| 250 | |
| 251 | return $x->round(@r) if $y->is_zero(); |
| 252 | |
| 253 | my $sign = 0; # sign of result |
| 254 | $sign = 1 if ($sx == -1) || ($sy == -1); |
| 255 | |
| 256 | my ($bx,$by); |
| 257 | |
| 258 | if ($sx == -1) # if x is negative |
| 259 | { |
| 260 | # two's complement: inc and flip all "bits" in $bx |
| 261 | $bx = $x->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc |
| 262 | $bx =~ s/-?0x//; |
| 263 | $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 264 | } |
| 265 | else |
| 266 | { |
| 267 | $bx = $x->as_hex(); # get binary representation |
| 268 | $bx =~ s/-?0x//; |
| 269 | $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 270 | } |
| 271 | if ($sy == -1) # if y is negative |
| 272 | { |
| 273 | # two's complement: inc and flip all "bits" in $by |
| 274 | $by = $y->copy()->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc |
| 275 | $by =~ s/-?0x//; |
| 276 | $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 277 | } |
| 278 | else |
| 279 | { |
| 280 | $by = $y->as_hex(); # get binary representation |
| 281 | $by =~ s/-?0x//; |
| 282 | $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 283 | } |
| 284 | # now we have bit-strings from X and Y, reverse them for padding |
| 285 | $bx = reverse $bx; |
| 286 | $by = reverse $by; |
| 287 | |
| 288 | # padd the shorter string |
| 289 | my $xx = "\x00"; $xx = "\x0f" if $sx == -1; |
| 290 | my $yy = "\x00"; $yy = "\x0f" if $sy == -1; |
| 291 | my $diff = CORE::length($bx) - CORE::length($by); |
| 292 | if ($diff > 0) |
| 293 | { |
| 294 | $by .= $yy x $diff; |
| 295 | } |
| 296 | elsif ($diff < 0) |
| 297 | { |
| 298 | $bx .= $xx x abs($diff); |
| 299 | } |
| 300 | |
| 301 | # or the strings together |
| 302 | my $r = $bx | $by; |
| 303 | |
| 304 | # and reverse the result again |
| 305 | $bx = reverse $r; |
| 306 | |
| 307 | # one of $x or $y was negative, so need to flip bits in the result |
| 308 | # in both cases (one or two of them negative, or both positive) we need |
| 309 | # to get the characters back. |
| 310 | if ($sign == 1) |
| 311 | { |
| 312 | $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/; |
| 313 | } |
| 314 | else |
| 315 | { |
| 316 | $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/; |
| 317 | } |
| 318 | |
| 319 | $bx = '0x' . $bx; |
| 320 | if ($CALC_EMU->can('_from_hex')) |
| 321 | { |
| 322 | $x->{value} = $CALC_EMU->_from_hex( \$bx ); |
| 323 | } |
| 324 | else |
| 325 | { |
| 326 | $r = $self->new($bx); |
| 327 | $x->{value} = $r->{value}; |
| 328 | } |
| 329 | |
| 330 | # if one of X or Y was negative, we need to decrement result |
| 331 | $x->bdec() if $sign == 1; |
| 332 | |
| 333 | $x->round(@r); |
| 334 | } |
| 335 | |
| 336 | sub __emu_bxor |
| 337 | { |
| 338 | my ($self,$x,$y,$sx,$sy,@r) = @_; |
| 339 | |
| 340 | return $x->round(@r) if $y->is_zero(); |
| 341 | |
| 342 | my $sign = 0; # sign of result |
| 343 | $sign = 1 if $x->{sign} ne $y->{sign}; |
| 344 | |
| 345 | my ($bx,$by); |
| 346 | |
| 347 | if ($sx == -1) # if x is negative |
| 348 | { |
| 349 | # two's complement: inc and flip all "bits" in $bx |
| 350 | $bx = $x->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc |
| 351 | $bx =~ s/-?0x//; |
| 352 | $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 353 | } |
| 354 | else |
| 355 | { |
| 356 | $bx = $x->as_hex(); # get binary representation |
| 357 | $bx =~ s/-?0x//; |
| 358 | $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 359 | } |
| 360 | if ($sy == -1) # if y is negative |
| 361 | { |
| 362 | # two's complement: inc and flip all "bits" in $by |
| 363 | $by = $y->copy()->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc |
| 364 | $by =~ s/-?0x//; |
| 365 | $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 366 | } |
| 367 | else |
| 368 | { |
| 369 | $by = $y->as_hex(); # get binary representation |
| 370 | $by =~ s/-?0x//; |
| 371 | $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; |
| 372 | } |
| 373 | # now we have bit-strings from X and Y, reverse them for padding |
| 374 | $bx = reverse $bx; |
| 375 | $by = reverse $by; |
| 376 | |
| 377 | # padd the shorter string |
| 378 | my $xx = "\x00"; $xx = "\x0f" if $sx == -1; |
| 379 | my $yy = "\x00"; $yy = "\x0f" if $sy == -1; |
| 380 | my $diff = CORE::length($bx) - CORE::length($by); |
| 381 | if ($diff > 0) |
| 382 | { |
| 383 | $by .= $yy x $diff; |
| 384 | } |
| 385 | elsif ($diff < 0) |
| 386 | { |
| 387 | $bx .= $xx x abs($diff); |
| 388 | } |
| 389 | |
| 390 | # xor the strings together |
| 391 | my $r = $bx ^ $by; |
| 392 | |
| 393 | # and reverse the result again |
| 394 | $bx = reverse $r; |
| 395 | |
| 396 | # one of $x or $y was negative, so need to flip bits in the result |
| 397 | # in both cases (one or two of them negative, or both positive) we need |
| 398 | # to get the characters back. |
| 399 | if ($sign == 1) |
| 400 | { |
| 401 | $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/; |
| 402 | } |
| 403 | else |
| 404 | { |
| 405 | $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/; |
| 406 | } |
| 407 | |
| 408 | $bx = '0x' . $bx; |
| 409 | if ($CALC_EMU->can('_from_hex')) |
| 410 | { |
| 411 | $x->{value} = $CALC_EMU->_from_hex( \$bx ); |
| 412 | } |
| 413 | else |
| 414 | { |
| 415 | $r = $self->new($bx); |
| 416 | $x->{value} = $r->{value}; |
| 417 | } |
| 418 | |
| 419 | # calculate sign of result |
| 420 | $x->{sign} = '+'; |
| 421 | $x->{sign} = '-' if $sx != $sy && !$x->is_zero(); |
| 422 | |
| 423 | $x->bdec() if $sign == 1; |
| 424 | |
| 425 | $x->round(@r); |
| 426 | } |
| 427 | |
| 428 | sub __emu_bsqrt |
| 429 | { |
| 430 | my ($self,$x,@r) = @_; |
| 431 | |
| 432 | # this is slow: |
| 433 | return $x->round(@r) if $x->is_zero(); # 0,1 => 0,1 |
| 434 | |
| 435 | return $x->bone('+',@r) if $x < 4; # 1,2,3 => 1 |
| 436 | my $y = $x->copy(); |
| 437 | my $l = int($x->length()/2); |
| 438 | |
| 439 | $x->bone(); # keep ref($x), but modify it |
| 440 | $x->blsft($l,10) if $l != 0; # first guess: 1.('0' x (l/2)) |
| 441 | |
| 442 | my $last = $self->bzero(); |
| 443 | my $two = $self->new(2); |
| 444 | my $lastlast = $self->bzero(); |
| 445 | #my $lastlast = $x+$two; |
| 446 | while ($last != $x && $lastlast != $x) |
| 447 | { |
| 448 | $lastlast = $last; $last = $x->copy(); |
| 449 | $x->badd($y / $x); |
| 450 | $x->bdiv($two); |
| 451 | } |
| 452 | $x->bdec() if $x * $x > $y; # overshot? |
| 453 | $x->round(@r); |
| 454 | } |
| 455 | |
| 456 | sub __emu_broot |
| 457 | { |
| 458 | my ($self,$x,$y,@r) = @_; |
| 459 | |
| 460 | return $x->bsqrt() if $y->bacmp(2) == 0; # 2 => square root |
| 461 | |
| 462 | # since we take at least a cubic root, and only 8 ** 1/3 >= 2 (==2): |
| 463 | return $x->bone('+',@r) if $x < 8; # $x=2..7 => 1 |
| 464 | |
| 465 | my $num = $x->numify(); |
| 466 | |
| 467 | if ($num <= 1000000) |
| 468 | { |
| 469 | $x = $self->new( int ( sprintf ("%.8f", $num ** (1 / $y->numify() )))); |
| 470 | return $x->round(@r); |
| 471 | } |
| 472 | |
| 473 | # if $n is a power of two, we can repeatedly take sqrt($X) and find the |
| 474 | # proper result, because sqrt(sqrt($x)) == root($x,4) |
| 475 | # See Calc.pm for more details |
| 476 | my $b = $y->as_bin(); |
| 3a427a11 |
477 | if ($b =~ /0b1(0+)$/) |
| b282a552 |
478 | { |
| 479 | my $count = CORE::length($1); # 0b100 => len('00') => 2 |
| 480 | my $cnt = $count; # counter for loop |
| 481 | my $shift = $self->new(6); |
| 482 | $x->blsft($shift); # add some zeros (even amount) |
| 483 | while ($cnt-- > 0) |
| 484 | { |
| 485 | # 'inflate' $X by adding more zeros |
| 486 | $x->blsft($shift); |
| 487 | # calculate sqrt($x), $x is now a bit too big, again. In the next |
| 488 | # round we make even bigger, again. |
| 489 | $x->bsqrt($x); |
| 490 | } |
| 491 | # $x is still to big, so truncate result |
| 492 | $x->brsft($shift); |
| 493 | } |
| 494 | else |
| 495 | { |
| 3a427a11 |
496 | # trial computation by starting with 2,4,6,8,10 etc until we overstep |
| 497 | my $step; |
| 498 | my $trial = $self->new(2); |
| 499 | my $two = $self->new(2); |
| 500 | my $s_128 = $self->new(128); |
| 501 | |
| 502 | local undef $Math::BigInt::accuracy; |
| 503 | local undef $Math::BigInt::precision; |
| 504 | |
| 505 | # while still to do more than X steps |
| 506 | do |
| 507 | { |
| 508 | $step = $self->new(2); |
| 509 | while ( $trial->copy->bpow($y)->bacmp($x) < 0) |
| 510 | { |
| 511 | $step->bmul($two); |
| 512 | $trial->badd($step); |
| 513 | } |
| 514 | |
| 515 | # hit exactly? |
| 516 | if ( $trial->copy->bpow($y)->bacmp($x) == 0) |
| 517 | { |
| 518 | $x->{value} = $trial->{value}; # make copy while preserving ref to $x |
| 519 | return $x->round(@r); |
| 520 | } |
| 521 | # overstepped, so go back on step |
| 522 | $trial->bsub($step); |
| 523 | } while ($step > $s_128); |
| 524 | |
| 525 | $step = $two->copy(); |
| 526 | while ( $trial->copy->bpow($y)->bacmp($x) < 0) |
| 527 | { |
| 528 | $trial->badd($step); |
| 529 | } |
| 530 | |
| 531 | # not hit exactly? |
| 532 | if ( $x->bacmp( $trial->copy()->bpow($y) ) < 0) |
| 533 | { |
| 534 | $trial->bdec(); |
| 535 | } |
| 536 | # copy result into $x (preserve ref) |
| 537 | $x->{value} = $trial->{value}; |
| b282a552 |
538 | } |
| 539 | $x->round(@r); |
| 540 | } |
| 541 | |
| 542 | sub __emu_as_hex |
| 543 | { |
| 544 | my ($self,$x,$s) = @_; |
| 545 | |
| 546 | return '0x0' if $x->is_zero(); |
| 547 | |
| 548 | my $x1 = $x->copy()->babs(); my ($xr,$x10000,$h,$es); |
| 549 | if ($] >= 5.006) |
| 550 | { |
| 551 | $x10000 = $self->new (0x10000); $h = 'h4'; |
| 552 | } |
| 553 | else |
| 554 | { |
| 555 | $x10000 = $self->new (0x1000); $h = 'h3'; |
| 556 | } |
| 557 | while (!$x1->is_zero()) |
| 558 | { |
| 559 | ($x1, $xr) = bdiv($x1,$x10000); |
| 560 | $es .= unpack($h,pack('v',$xr->numify())); |
| 561 | } |
| 562 | $es = reverse $es; |
| 563 | $es =~ s/^[0]+//; # strip leading zeros |
| 564 | $s . '0x' . $es; |
| 565 | } |
| 566 | |
| 567 | sub __emu_as_bin |
| 568 | { |
| 569 | my ($self,$x,$s) = @_; |
| 570 | |
| 571 | return '0b0' if $x->is_zero(); |
| 572 | |
| 573 | my $x1 = $x->copy()->babs(); my ($xr,$x10000,$b,$es); |
| 574 | if ($] >= 5.006) |
| 575 | { |
| 576 | $x10000 = $self->new (0x10000); $b = 'b16'; |
| 577 | } |
| 578 | else |
| 579 | { |
| 580 | $x10000 = $self->new (0x1000); $b = 'b12'; |
| 581 | } |
| 582 | while (!$x1->is_zero()) |
| 583 | { |
| 584 | ($x1, $xr) = bdiv($x1,$x10000); |
| 585 | $es .= unpack($b,pack('v',$xr->numify())); |
| 586 | } |
| 587 | $es = reverse $es; |
| 588 | $es =~ s/^[0]+//; # strip leading zeros |
| 589 | $s . '0b' . $es; |
| 590 | } |
| 591 | |
| 592 | ############################################################################## |
| 593 | ############################################################################## |
| 594 | |
| 595 | 1; |
| 596 | __END__ |
| 597 | |
| 598 | =head1 NAME |
| 599 | |
| 600 | Math::BigInt::CalcEmu - Emulate low-level math with BigInt code |
| 601 | |
| 602 | =head1 SYNOPSIS |
| 603 | |
| 604 | Contains routines that emulate low-level math functions in BigInt, e.g. |
| 605 | optional routines the low-level math package does not provide on it's own. |
| 606 | |
| 607 | Will be loaded on demand and automatically by BigInt. |
| 608 | |
| 609 | Stuff here is really low-priority to optimize, |
| 610 | since it is far better to implement the operation in the low-level math |
| 611 | libary directly, possible even using a call to the native lib. |
| 612 | |
| 613 | =head1 DESCRIPTION |
| 614 | |
| 615 | =head1 METHODS |
| 616 | |
| 617 | =head1 LICENSE |
| 618 | |
| 619 | This program is free software; you may redistribute it and/or modify it under |
| 620 | the same terms as Perl itself. |
| 621 | |
| 622 | =head1 AUTHORS |
| 623 | |
| 624 | (c) Tels http://bloodgate.com 2003 - based on BigInt code by |
| 625 | Tels from 2001-2003. |
| 626 | |
| 627 | =head1 SEE ALSO |
| 628 | |
| 629 | L<Math::BigInt>, L<Math::BigFloat>, L<Math::BigInt::BitVect>, |
| 630 | L<Math::BigInt::GMP> and L<Math::BigInt::Pari>. |
| 631 | |
| 632 | =cut |
projects / p5sagit/p5-mst-13.2.git / blame